[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 496

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There is a problem for economists and marketers. I will say right away that it is related to my work, I have not found an analytical solution, in principle I can get by with manual calculations, but I wonder if the problem can be solved.

So, there is a formula from a book by a famous marketing analyst (I will not mention his name), which shows how much (what percentage) should increase sales to the customer at a lower price (discount), so that the mass profit deal has not decreased from the initially planned level.

O = P / (P - P) x 100%,

where O is the necessary increase in sales (as a percentage);

P - percentage of change (decrease) in prices;

P - share of profit in the price of the product.

Practice has shown that the formula is incorrect and gives large deviations from the truth for some values of the arguments. I made a correct calculation in the Excel file and compared it with the incorrect data. The "Inconsistencies" worksheet shows how wrong the formula is.

Can this formula be made correct by having the same as the arguments: the customer discount and the initial product margin? It seems that the dependence of these quantities is non-linear, and can this be expressed analytically in a single formula? And make a table like in Excel, but with the correct values.

 

The relationship here is also non-linear, depending on the discount.

Let the price without the discount be Price, and the sales volume be Volume0. Unit cost is equal to Price*(1-P). The total net profit is equal to Price*P*Volume0.

We make a discount of P. The price is now Price*(1-P) and the cost is the same. Therefore, total net profit equals Price*(P-P)*Volume1.

Equating the total net profits, we get: Price*(P-P)*Volume1 = Price*P*Volume0.

Hence Volume1/Volume0 = P/(P-P).

And the required growth in sales in % is equal to (Volume1/Volume0 - 1)*100% = (P/(P-P) - 1)*100% = P/(P-P)*100%.

So this is correct. Check it again.

P.S. I haven't looked at the attachment.

 

Mathemat, thank you!

While I'm thinking about your deductions, here's a practical example with a calculation that got me thinking.



You can see that the formula gives the wrong value. And I gave the correct calculation in the file attached to the previous post.

 
In short, the formula doesn't work.
 
That's it, I've got the catch. The percentage change in P only applies to the volume in pieces. And I tried to apply it to the volume in money. In this case, the formula doesn't work.
 

Процентное изменение Р относится только к объему в штуках. А я его попробовал применить к объему в деньгах.

You must have meant O, not R?

 
Yeah, that's right. Totally confused about that formula. Thanks again.
 

From matforum:

Как закрасить на доске 9×9 наименьшее количество клеток так, чтобы из центра доски не были видны её края (сиречь, любой луч, выходящий из центра, задевал какую-нибудь закрашенную клетку хотя бы по углу)?

* It is forbidden to colour in cells adjacent to a side or corner, as well as the centre cell.

The incomplete solution I posted there is best left unseen. It's more interesting.

P.S. First try to get some solution, not necessarily "minimal". The main condition: the shaded cells must not touch each other, even only in one point.

 

Another one, but from the Olympics:

Среди чисел a, b, c есть два одинаковых. А оставшееся число - другое. Составьте такое арифметическое выражение из букв a, b, c, знаков +, -, *, : и скобок, чтобы в результате вычислений получилось это число. (Скобки, знаки и буквы можно использовать любое количество раз.)

 
Mathemat:

Another one, but from the Olympics:

Is the root allowed?
1...489490491492493494495496497498499500501502503...628
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